An object of mass 40 kg and having velocity `4 ms^(-1)` collides with another object of mass 60 kg. having velocity 2 ` m s^(-1)` The loss of kinetic energy when the collision is perfectly ineleastic is

Options

A. 392 J
B. 440 j
C. 48 J
D. 110 J

Answer

C

Explanation

Here, ` m_(1) = 40 kg , u_(1) = 4 m s^(-1)`
`m_(2) = 60 kg , u_(2) = m s^(-1)`
According to law of conservation of linear momentum, we get
` (m_(1) + m_(2))v = m_(1)u_(1) + m_(2)u_(2)`
` v = ( m_(1)u_(1)+m_(1)u_(2))/( m_(1)+m_(2)) = (40 xx 4 + 60 xx 2)/(40 + 60 ) = 2.8 m s^(-1) `
Loss in KE = ` 1/2 m_(1)u_(1)^(2) + 1/2 m_(2)u_(2)^(2) - 1/2 (m_(1) + m_(2))v^(2)`
`1/2 [40 xx 16 + 60 xx 4 - 100 xx 2.8^(2)] = 48 J `